
On the completeness of spider diagrams augmented with constands / Gem Stapleton...[et al.]. A practicebased approach to diagrams (review)In SunJoo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams, Birkhaüser. 2013.

8Experimenting with TrianglesAxiomathes 32 (1): 5577. 2022.Is there anything like an experiment in mathematics? And if this is the case, what would distinguish a mathematical experiment from a mathematical thought experiment? In the present paper, a framework for the practice of mathematics will be put forward, which will consider mathematics as an experimenting activity and as a proving activity. The relationship between these two activities will be explored and more importantly a distinction between thoughtexperiments, real experiments, quasi experim…Read more

Diagrammatic Representation and Inference. 13th International Conference, Diagrams 2022, Rome, Italy, September 14–16, 2022, Proceedings (edited book)Springer, Cham. 2022.

6Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientae 16 511. 2012.

126Introduction: Varieties of IconicityReview of Philosophy and Psychology 6 (1): 125. 2015.This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of repres…Read more

39Manipulative imagination: how to move things around in mathematicsTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 345360. 2018.In the first part of the paper, previous work about embodied mathematics and the practice of topology will be presented. According to the proposed view, in order to become experts, topologists have to learn how to use manipulative imagination: representations are cognitive tools whose functioning depends from preexisting cognitive abilities and from specific training. In the second part of the paper, the notion of imagination as “makebelieve” is discussed to give an account of cognitive tools …Read more

308Tools for Thought: The Case of MathematicsEndeavour 2 (42): 172179. 2018.The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be …Read more

23Review of Frederik Stjernfelt, Diagrammatology: An Investigation on the Borderlines of Phenomenology, Ontology and Semiotics (review)Notre Dame Philosophical Reviews 2008 (7). 2008.

32Gabriele Lolli. Fenomenologia della dimostrazione. Turin: Il Mulino, 2005. ISBN 8833915883. Pp. 182Philosophia Mathematica 15 (1): 132134. 2007.In his book Gabriele Lolli discusses the notion of proof, which is, according to him, the most important and at the same time the least studied aspect of mathematics. According to Lolli, a theorem is a conditional sentence of the form ‘if T then A’ such that A is a logical consequence of T, where A is a sentence and T is a sentence or a conjunction or set of sentences. Verifying that A is a consequence of T generally involves considering infinitely many interpretations; so it is something which …Read more

39Mohan Matthen seeing, doing and knowing: A philosophical theory of sense perception oxford: Oxford university press, 2005 hardback £40.00 ISBN: 0199268509 (review)British Journal for the Philosophy of Science 57 (4): 781783. 2006.

27Giaquinto, Marcus. Visual Thinking in Mathematics: An Epistemological StudyReview of Metaphysics 66 (1): 148150. 2012.

Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 (1): 511. 2012.

694Envisioning Transformations – The Practice of TopologyIn Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 20122014, Birkhäuser. pp. 2550. 2016.The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp deﬁnition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the pra…Read more

200Geometria, ragionamento e scommesseIn University of Urbino © Isonomia – Epistemologica (ed.), Mettere a fuoco il mondo, . pp. 3646. 2014.Poiché i miei interessi di ricerca si concentrano sul rapporto tra spazio e rappresentazione, nel presente articolo commenterò un lavoro di Achille C. Varzi pubblicato nel 2008 e intitolato, nella sua versione italiana, «Configurazioni, regole e inferenze». Accennerò anche a un secondo articolo scritto da Varzi e Massimo Warglien e pubblicato nel 2003, intitolato «The Geometry of Negation». Mi rivolgerò poi alla psicologia sperimentale, collegando alcuni aspetti delle osservazioni di Varzi…Read more

28Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientae 16 511. 2012.

39Arturo Carsetti • seeing, thinking and knowing: Meaning and selforganisation in visual cognition and thought • dordrecht, the netherlands: Kluwer academic publishers, • 2004 • hardback £97.00 • isbn: 1402020805 (review)British Journal for the Philosophy of Science 57 (3): 623625. 2006.

276Intuition and visualization in mathematical problem solvingTopoi 29 (1): 2939. 2010.In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical …Read more

627An Inquiry into the Practice of Proving in LowDimensional TopologyIn Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice, Springer International Publishing. pp. 315336. 2015.The aim of this article is to investigate speciﬁc aspects connected with visualization in the practice of a mathematical subﬁeld: lowdimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in lowdimensional topology, justiﬁcations can be based on sequences of pictures. Three these…Read more

24Review of M. Giaquinto, Visual Thinking in Mathematics: An Epistemological Study (review)Review of Metaphysics 66 (1): 148150. 2012.

6Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 511. 2012.

950Forms and Roles of Diagrams in Knot TheoryErkenntnis 79 (4): 829842. 2014.The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must develop a s…Read more

Centre National de la Recherche ScientifiqueArchives HenriPoincaré  Philosophie Et Recherches Sur Les Sciences Et Les TechnologiesChargé de Recherche
